Apple Pi Activity – Optional Assessment
Third Marking Period
Name___________________
Period____Date__________
You will need:
•Piece of string, approximately 48” long
•Ruler
•6 or more flat circular objects to be measured;
don’t use ones that are too large or too small
(you’ll have difficulties measuring them)
•Calculator
Answer these questions:
What do we call the distance around the outside of an
object?______________________
What is the distance around the outside of a circle known as?_______________________
What is the formula for finding the distance around the outside of a circle? _______________
Apple Pi Activity
(1) On white paper, trace the circular objects you selected for this activity; label what they are, for example, a
lid, a cup, a small bowl, etc.
(2) On the actual objects, not the drawings: for each circular object, you will need to measure the distance
around and the distance across. (You can use the piece of string to measure around the object; to ensure
accuracy, keep the string taut when measuring.) Then stretch the string along a ruler and note the length. When
measuring the distance across, place the ruler so that it passes through the center – this is like measuring a
diameter of a circle.
(3) Complete the Pi Recording Chart on page 2, using your measurements. Be sure to include a description of
each object as well as the units for each.
•A calculator can be used to divide the distance around by the distance across.
•If any numbers in the last column seem irregular, check your measurements.
•Answer both questions on the worksheet.
Apple Pi Recording Chart
NAME ___________________________
Using string and rulers, measure the distance around several round objects, as well as the distance across the
middle of those objects. Record your measurements below.
OBJECT
DISTANCE AROUND
THE OUTSIDE OF THE
OBJECT
DISTANCE ACROSS
THE MIDDLE OF
THE OBJECT
DISTANCE AROUND
DIVIDED BY
DISTANCE ACROSS
Remember: Include appropriate labels on all measurements!(you can use inches or centimeters)
1. What do you notice about the numbers in the last column?
2. What is the average of all values in the last column?
Post Apple Pi Activity Assessment
Name__________________________________________
Due Date ________________________ Period ________
A. Summary Questions:
1. What does it mean to say that π is a ratio? What is being compared?
2. Does the ratio of circumference to diameter vary depending on the size of the circle or the unit of
measurement?
3. Why did we use the ratio of circumference to diameter for several objects?
4. Were any of the ratios in the last column not close to 3.14? Explain why this might have happened.
5. Based on your findings, what is the formula for finding the circumference of a circle?
6. According to Guinness, the world’s largest rice cake measured 5.83 feet in diameter. What is the
circumference of this rice cake?
7. The tallest tree in the world is believed to be the Mendicino Tree, a redwood near Ukiah, California, that
is 112 meters tall! Near the ground, the circumference of the tree is about 9.85 meters. The age of the
redwood can be estimated by comparing its diameter to trees with similar diameters. What is the
diameter of the Mendicino Tree?
B. Graphing Results from Pi Activity
•You must create a graph using the data from the Pi Activity Chart (graph paper is on the next page.)
•The diameters of the objects should be plotted along the horizontal axis of the graph and the circumferences
should be plotted along the vertical axis.
•Create a scatterplot by graphing the points from your chart
•Draw a line of best fit; a straight line that approximates the points on your graph; (locate this line so that it goes
through the approximate middle of all the points.)
•Identify two points on the line and determine the vertical difference and the horizontal difference between the
two points:
Vertical Difference_______________
Horizontal Difference__________________
•Divide the vertical difference by the horizontal difference. What is your result?
•For the line in your graph, where does the y-intercept occur? Where should the y-intercept occur?
Explain what the y-intercept means in terms of diameter and circumference.
•If slope is defined as the steepness of a line and it is calculated by vertical change over horizontal change,
what is the slope of your graph? Write your answer in fraction form.
How does the slope of your line compare to the decimal approximation of π?
Pi Activity Scoring
Name _____________________________ Period ______ Date _____________
Optional: Partner’s Name _____________________ Period ________
(Neatness counts!)
Page 1: Answer questions; do the tracings of the six (or more) objects you
will be using; be sure to label what they are i.e. cup, lid, bowl, etc.
(3) points possible ______
Page 2: Pi Recording Chart; you may use a calculator for the answers for
the column entitled “The distance around divided by the distance across”;
answers for questions 1 and 2.
(3) points possible _______
Page 3: Answers for questions A, 1 – 7 (nicely written:
full sentences; check grammar/spelling/punctuation)
(3) points possible ________
Pages 4 – 5: Graphing exercises: p. 4 answer the questions;
p. 5, make your graph. Be sure to include labels for the two
axes, and a title for your graph. Indicate the two points you
used to find the distance between the Y coordinates and the
distance between the X coordinates.
(4, 12)
(3) points possible ________
12 – 5 = 7
4–2
2
(2, 5)
Difference of the Ys
Difference of the Xs